Problem: Find the greatest common factor of $56, 28,$ and $14$.
Explanation: The greatest common factor (GCF) is the largest number that is a factor of $56, 28,$ and $14$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}56 &=2\cdot2\cdot2\cdot7\\\\\\\\ 28&=2\cdot2\cdot7\\\\\\\\ 14&=2\cdot7 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}56 &=2\cdot2\cdot2\cdot7\\\\\\\\ 28&=2\cdot2\cdot7\\\\\\\\ 14&=2\cdot7 \end{aligned}$ Each number shares the factors ${2}$ and ${7},$ so the GCF is $2\cdot7={14}$. The greatest common factor of $56, 28,$ and $14$ is $14$.